International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 3, Pages 173-177
doi:10.1155/S0161171200003252

Approximating fixed points of nonexpansive mappings

Guimei Liu1 , Deng Lei2 and Shenghong Li1

1Department of Mathematics, Zhejiang University, Zhejiang, 310027, China
 2Department of Mathematics, Southwest China Normal University, Beibei, Chongqing 400715, China

Abstract

We consider a mapping S of the form S=α0I+α1T1+α2T2+⋯+αkTk, where αi≥0, α0>0, α1>0 and ∑i=0kαi=1. We show that the Picard iterates of S converge to a common fixed point of Ti(i=1,2,…,k)in a Banach space when Ti(i=1,2,…,k) are nonexpansive.